If `sqrt(2)=1.4142` then the approximate value of `sqrt(2/9)` is

Options

A. 0.2321
B. 0.4714
C. 0.3714
D. 0.4174

Answer

To find the approximate value of \( \sqrt{\frac{2}{9}} \) given that \( \sqrt{2} = 1.4142 \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression \( \sqrt{\frac{2}{9}} \). We can rewrite this using the property of square roots:

\[ \sqrt{\frac{2}{9}} = \frac{\sqrt{2}}{\sqrt{9}} \]

### Step 2: Simplify \( \sqrt{9} \)
Next, we know that \( \sqrt{9} = 3 \). So we can substitute this into our expression:

\[ \frac{\sqrt{2}}{\sqrt{9}} = \frac{\sqrt{2}}{3} \]

### Step 3: Substitute the value of \( \sqrt{2} \)
Now, we substitute the given value of \( \sqrt{2} \):

\[ \frac{\sqrt{2}}{3} = \frac{1.4142}{3} \]

### Step 4: Perform the division
Now we need to divide \( 1.4142 \) by \( 3 \):

\[ \frac{1.4142}{3} \approx 0.4714 \]

### Conclusion
Thus, the approximate value of \( \sqrt{\frac{2}{9}} \) is \( 0.4714 \).

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